Problem: Simplify the following expression: $\dfrac{63x^5}{54x^5}$ You can assume $x \neq 0$.
$ \dfrac{63x^5}{54x^5} = \dfrac{63}{54} \cdot \dfrac{x^5}{x^5} $ To simplify $\frac{63}{54}$ , find the greatest common factor (GCD) of $63$ and $54$ $63 = 3 \cdot 3 \cdot 7$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(63, 54) = 3 \cdot 3 = 9 $ $ \dfrac{63}{54} \cdot \dfrac{x^5}{x^5} = \dfrac{9 \cdot 7}{9 \cdot 6} \cdot \dfrac{x^5}{x^5} $ $\phantom{ \dfrac{63}{54} \cdot \dfrac{5}{5}} = \dfrac{7}{6} \cdot \dfrac{x^5}{x^5} $ $ \dfrac{x^5}{x^5} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x \cdot x \cdot x \cdot x} = 1 $ $ \dfrac{7}{6} \cdot 1 = \dfrac{7}{6} $